Compact ultrafast (ps or fs) fiber-based pulsed sources, particular in the visible and ultraviolet (UV) portions of the electromagnetic spectrum, are in high demand for such applications as ultrafast spectroscopy, fluorescence spectroscopy, photochemistry and photophysics, multiphoton microscopy, fluorescence lifetime imaging, non-linear biomedical imaging, and precision optical frequency metrology. As an example, many fluorescent molecules of biomedical importance allow one-photon excitation within the 350-600 nm spectral range and two-photon excitation within the 500-700 nm spectral range. Desirable pulse properties, such as those of pulse duration, energy per pulse, and repetition rate, are more readily available in infrared sources, thus it is useful to up-convert infrared pulses into the visible while retaining, if not enhancing, requisite spectral and temporal characteristics.
Many applications, such as multiphoton microscopy and ultrafast spectroscopy, require narrowband ultrashort (<5 ps) pulses of a few milliwatts of average power that are widely tunable across a frequency up-converted region of the pump laser. While selective spectral filtering of the supercontinuum may lead to a useful multi-wavelength pulsed source, the elongated temporal width and the decreased pulse energy produce unavoidable adverse effects. The more attractive solution is to efficiently convert input pump power into the targeted spectral band (signal) using fiber-based nonlinear frequency up-conversion techniques.
Photonic crystal fibers (PCFs), optical waveguides exhibiting tailored group velocity dispersion and enhanced modal confinement (and thus concomitantly enhanced nonlinearity) have proven a convenient medium in which to achieve desired up-conversion and other non-linear processes. Numerous efforts have employed femtosecond pump lasers to generate broadband and flat supercontinuum output from PCFs with a power level on the order of tens of milliwatts. A survey of the state of the art may be found in the review paper of Dudley et al., Supercontinuum Generation in Photonic Crystal Fiber, Rev. Mod. Phys., vol. 78, pp. 1135-84 (2006), which is incorporated herein by reference. The material and geometry of PCFs governs the zero dispersion wavelength (ZDW) of the fiber, which, in tapered fibers, may be varied as a function of length of the fiber.
One technique for up-conversion in a fiber is four-wave mixing excited at the slightly normal dispersion regime of the fiber (where the refractive index increases with frequency), which has been implemented in the form of an optical parametric oscillator. Wide tunability of the signal wavelength in the near-infrared and the visible can be achieved by tuning the pump wavelength across a relatively narrow (˜20 nm) spectral region. Nonetheless, the pulse walk-off effect and the supercontinuum onset have largely restricted the pump-to-signal conversion efficiency on the order of 2%, thus preventing the generation of a multimilliwatt-level signal.
Propagation of waves in a PCF may be described by a generalized nonlinear Schroedinger equation (GNLSE), solutions of which include solitons that maintain their shape as they propagate in the fiber. Akhmediev et al., Cherenkov radiation emitted by solitons in optical fibers, Phys. Rev. A, vol. 51, pp. 2602-07 (1995), incorporated herein by reference, established that, under certain conditions, a soliton generates a dispersive wave in a process equivalent to a Cherenkov radiation process in the frame of reference of commoving time t and the propagation direction z of the soliton. Cherenkov radiation (CR) mediated by fiber solitons may also be referred to as dispersive wave generation, non-solitonic radiation, or soliton-induced resonant emission.
The feasibility of four wave mixing (FWM) in optical fibers has been pursued in several studies using single-mode FWM. In single-mode FWM, the pump, idler, and signal propagate in the same fiber mode. Sharping et al., Four-wave Mixing in Microstructure Fiber, Opt. Lett., vol. 26, pp. 1048-50 (2001) described a highly nonlinear PCF with a deeply blue-shifted zero dispersion wavelength (ZDW), in which FWM was generated with a relatively small Stokes-shift (400 cm−1). The Stokes-shift can be enlarged to 6000 cm−1 by tapering a PCF to generate 535-570 nm anti-Stokes pulses, as described by Abedin et al., Highly nondegenerate femtosecond four-wave mixing in tapered microstructure fiber, Appl. Phys. Lett., vol. 89, 171118 (2006). However, the two foregoing studies require seeding the Stokes field so that two collinear laser beams, corresponding to both the pump as well as the Stokes fields, must be incident on the fiber.
It has also been shown to be possible, for sufficiently large pump intensity, to amplify the FWM signal from quantum perturbation without seeding the idler externally. This has been achieved in a higher-order fiber mode of specially designed PCFs (i.e., the pump, signal and idler are generated in the same higher-order fiber mode rather than the fundamental fiber mode) to produce a 600-nm signal, as described by Konorov et al., Generation of femtosecond anti-Stokes pulses through phase-matched parametric four-wave mixing in a photonic crystal fiber, Opt. Lett., vol. 29, 1545-47 (2004).
A disadvantage, however, of this operation is that offset pumping has to be employed to selectively excite the higher-order mode, significantly impairing the free-space-to-fiber coupling efficiency and achieving pump-to-signal conversion efficiencies of only 2%. More importantly, the wavelength-conversion selectivity of FWM is compromised by the presence of other nonlinear optical processes which promote supercontinuum (SC) generation. The SC contamination becomes more severe if the pump wavelength lies in the vicinity of the ZDW of the fiber, however such proximity to the ZDW is required for the phase-matching condition of the single-mode FWM.
One way in which FWM may be achieved absent SC contamination is to pump the fiber in a deeply normal dispersion regime and fulfill the phase-matching condition using different fiber modes. Such approach, termed intermodal FWM, was reported by Stolen et al., Appl. Phys. Lett., vol. 24, pp. 308-10 (1974) in conventional multimode fiber. Intermodal FWM was also realized by Lin et al., Appl. Phys. Lett., vol. 38, pp. 479-81 (1981) in specifically Ge-doped circular fibers pumped by 25-ps 532-nm pulses, suggesting that a series of Stokes-shifts up to 4300 cm−1 could be obtained by a series of properly designed fibers. However, this feasibility has not been further pursued possibly because the FWM is unstable over time due to the well-known photosensitivity of the Ge dopant.
CR has been invoked for tunable frequency up-conversion and/or a multimilliwatt signal. Knox and co-workers introduced submillimeter-scale dispersion micromanagement into a short (˜1 cm) PCF to generate femtosecond visible pulses from a Ti:sapphire laser. Unfortunately, the wavelength tunability of the pulses required a series of PCFs with different dispersion designs and a dedicated fiber-tapering facility (including a CO2 laser) to fabricate. As to the underlying mechanism, the individual roles of CR and four-wave mixing remain rather unclear.
Leitenstorfer and co-workers used a dispersion-shifted germanosilicate fiber to up-convert the 1.55 μm wavelength of an amplified femtosecond Er:fiber laser into the 1130-1300 nm region, and then frequency-doubled into the 520-700 nm visible region. Wavelength tunability was achieved by tuning the chirp of the pump laser, and conversion efficiencies as high as 30% were described. However, the germanosilicate fiber employed requires special dispersion engineering and may be susceptive to structural change due to its well-known photosensitivity. Additionally, the technique demands both a specially-designed pump laser, and in the case of the visible signal, a specific frequency-doubling crystal. A more broadly application technology that can use a wider range of tunable infrared pump lasers and more general-purpose PCFs is thus desirable.
Zheltikov and co-workers invoked CR from birefringent PCFs to frequency up-convert the 820-nm and 1.24-μm pump wavelengths into the visible region. Although the birefringence of fibers allows for production of different frequency-shifted signals, the signal wavelength is not strictly tunable both because of a limited tuning range and because the broadened signal spectrum. A strictly tunable up-conversion system is thus desirable.
While switching the pump polarization can lead to slight tunability of the CR wavelength, a technology is desirable that provides tunability by virtue of tuning the pump wavelength, even at high pump power. Unfortunately, increased pump powers tend to initiate supercontinuum around the signal band and, therefore, compromise the pump-to-signal conversion selectivity. One explanation of the emergence of the supercontinuum is that sequentially ejected red-shifted fundamental solitons emit a mixture of resonant blue-shifted CR of distinct frequencies, as postulated by Herrmann et al., Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers, Phys. Rev. Lett., vol. 88, No. 173901 (2002), which is incorporated herein by reference. Thus, CR has been considered as one mechanism initiating the blue edge of the supercontinuum, and at moderate pump powers, has appeared more as an irregular broadband feature than a narrowband line profile. It would be far more desirable, however, to provide supercontinuum-free widely-tunable multimilliwatt CR with a narrowband line profile that effectively extends the near-infrared emission wavelengths of a Ti:sapphire laser or a Yb-based laser, for example, to the UV-visible region.